Question

What composition transformation rule has ALMN, L (1,1), M (7,2), and N (5,7) map onto AL" M " N" , L" (2, -1), M " (-4, 0), and N " (-2,5)? (1 point)
O a reflection across the y-axis and a move to the left by 5 and up by 3
a reflection across the y-axis and a
• move to the right by 3 and down by 2
a rotation of 270 degrees
• clockwise and a move right by 3
and up by 2
a reflection across the x-axis and a
• move to the left by 3 and down by 2

Answer 1

To determine which transformation maps points L, M, and N to L", M", and N", we can analyze the given coordinates:

1. **Original Points:**
- L (1, 1)
- M (7, 2)
- N (5, 7)

2. **Transformed Points:**
- L" (2, -1)
- M" (-4, 0)
- N" (-2, 5)

Next, let’s break down the transformations that might occur between the original points and the transformed points.

### Analyzing Each Transformation Option:
1. **Reflection across the y-axis and a move to the left by 5 and up by 3:**
- Reflect across the y-axis:
- L (1, 1) → L' (-1, 1)
- M (7, 2) → M' (-7, 2)
- N (5, 7) → N' (-5, 7)
- Move left by 5 (subtract 5 from x) and up by 3 (add 3 to y):
- L' → L'' (-1 - 5, 1 + 3) = (-6, 4)
- M' → M'' (-7 - 5, 2 + 3) = (-12, 5)
- N' → N'' (-5 - 5, 7 + 3) = (-10, 10)
- This does not match the transformed points.

2. **Reflection across the y-axis and a move to the right by 3 and down by 2:**
- Same reflection gives:
- L' (-1, 1)
- M' (-7, 2)
- N' (-5, 7)
- Move right by 3 (add 3 to x) and down by 2 (subtract 2 from y):
- L' → L'' (-1 + 3, 1 - 2) = (2, -1)
- M' → M'' (-7 + 3, 2 - 2) = (-4, 0)
- N' → N'' (-5 + 3, 7 - 2) = (-2, 5)
- This matches the transformed points L", M", N".

3. **Rotation of 270 degrees clockwise and a move right by 3 and up by 2:**
- A 270-degree rotation (or -90-degree rotation):
- L (1, 1) → L' (1, -1)
- M (7, 2) → M' (2, -7)
- N (5, 7) → N' (7, -5)
- Then apply the move:
- L' → L'' (1 + 3, -1 + 2) = (4, 1)
- M' → M'' (2 + 3, -7 + 2) = (5, -5)
- N' → N'' (7 + 3, -5 + 2) = (10, -3)
- This does not match the transformed points.

4. **Reflection across the x-axis and a move to the left by 3 and down by 2:**
- Reflect across the x-axis:
- L (1, 1) → L' (1, -1)
- M (7, 2) → M' (7, -2)
- N (5, 7) → N' (5, -7)
- Move left by 3 and down by 2:
- L' → L'' (1 - 3, -1 - 2) = (-2, -3)
- M' → M'' (7 - 3, -2 - 2) = (4, -4)
- N' → N'' (5 - 3, -7 - 2) = (2, -9)
- This does not match the transformed points.

### Conclusion:
The transformation that maps points L, M, N onto L", M", and N" is the **reflection across the y-axis and a move to the right by 3 and down by 2**.

The answer is:
**a reflection across the y-axis and a move to the right by 3 and down by 2.**